\contentsline {chapter}{{Abstract}}{ii}
\contentsline {chapter}{{Preface}}{iii}
\contentsline {chapter}{{Table of Contents}}{iv}
\contentsline {chapter}{{List of Tables}}{vi}
\contentsline {chapter}{{List of Figures}}{vii}
\contentsline {chapter}{{List of Symbols}}{viii}
\contentsline {chapter}{{Acknowledgements}}{xi}
\contentsline {chapter}{{Dedication}}{xii}
\contentsline {chapter}{\numberline {1}{Introduction}}{1}
\contentsline {section}{\numberline {1.1}{Essential Dimension via Birational Geometry}}{2}
\contentsline {section}{\numberline {1.2}{Finite Groups of Essential Dimension $2$}}{3}
\contentsline {section}{\numberline {1.3}{Essential Dimension of $A_7$ and $S_7$}}{5}
\contentsline {section}{\numberline {1.4}{Overview}}{5}
\contentsline {chapter}{\numberline {2}{Del Pezzo Surfaces of Degree $\le 4$}}{7}
\contentsline {section}{\numberline {2.1}{Alternative Proofs}}{9}
\contentsline {subsection}{\numberline {2.1.1}{Del Pezzo Surfaces of Degree $4$}}{9}
\contentsline {subsection}{\numberline {2.1.2}{Del Pezzo Surfaces of Degree $3$}}{10}
\contentsline {chapter}{\numberline {3}{Conclusion}}{18}
\contentsline {section}{\numberline {3.1}{Applications}}{18}
\contentsline {section}{\numberline {3.2}{Future Research}}{19}
